I. Ekmark, M. Hoppe, T. Fülöp, P. Jansson, L. Antonsson, O. Vallhagen, I. Pusztai
{"title":"Fluid and kinetic studies of tokamak disruptions using Bayesian optimization","authors":"I. Ekmark, M. Hoppe, T. Fülöp, P. Jansson, L. Antonsson, O. Vallhagen, I. Pusztai","doi":"10.1017/s0022377824000606","DOIUrl":"https://doi.org/10.1017/s0022377824000606","url":null,"abstract":"When simulating runaway electron dynamics in tokamak disruptions, fluid models with lower numerical cost are often preferred to more accurate kinetic models. The aim of this work is to compare fluid and kinetic simulations of a large variety of different disruption scenarios in ITER. We consider both non-activated and activated scenarios; for the latter, we derive and implement kinetic sources for the Compton scattering and tritium beta decay runaway electron generation mechanisms in our simulation tool <jats:sc>Dream</jats:sc> (Hoppe <jats:italic>et al.</jats:italic>, <jats:italic>Comput. Phys. Commun.</jats:italic>, vol. 268, 2021, 108098). To achieve a diverse set of disruption scenarios, Bayesian optimization is used to explore a range of massive material injection densities for deuterium and neon. The cost function is designed to distinguish between successful and unsuccessful disruption mitigation based on the runaway current, current quench time and transported fraction of the heat loss. In the non-activated scenarios, we find that fluid and kinetic disruption simulations can have significantly different runaway electron dynamics, due to an overestimation of the runaway seed by the fluid model. The primary cause of this is that the fluid hot-tail generation model neglects superthermal electron transport losses during the thermal quench. In the activated scenarios, the fluid and kinetic models give similar predictions, which can be explained by the significant influence of the activated sources on the runaway dynamics and the seed.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"51 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alistair M. Arnold, Pavel Aleynikov, Boris N. Breizman
{"title":"Parallel expansion of a fuel pellet plasmoid","authors":"Alistair M. Arnold, Pavel Aleynikov, Boris N. Breizman","doi":"10.1017/s0022377824000588","DOIUrl":"https://doi.org/10.1017/s0022377824000588","url":null,"abstract":"The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"53 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices","authors":"Andrew Giuliani","doi":"10.1017/s0022377824000412","DOIUrl":"https://doi.org/10.1017/s0022377824000412","url":null,"abstract":"Many stellarator coil design problems are plagued by multiple minima, where the locally optimal coil sets can sometimes vary substantially in performance. As a result, solving a coil design problem a single time with a local optimization algorithm is usually insufficient and better optima likely do exist. To address this problem, we propose a global optimization algorithm for the design of stellarator coils and outline how to apply box constraints to the physical positions of the coils. The algorithm has a global exploration phase that searches for interesting regions of design space and is followed by three local optimization algorithms that search in these interesting regions (a ‘global-to-local’ approach). The first local algorithm (phase I), following the globalization phase, is based on near-axis expansions and finds stellarator coils that optimize for quasisymmetry in the neighbourhood of a magnetic axis. The second local algorithm (phase II) takes these coil sets and optimizes them for nested flux surfaces and quasisymmetry on a toroidal volume. The final local algorithm (phase III) polishes these configurations for an accurate approximation of quasisymmetry. Using our global algorithm, we study the trade-off between coil length, aspect ratio, rotational transform and quality of quasi-axisymmetry. The database of stellarators, which comprises approximately 200 000 coil sets, is available online and is called QUASR, for ‘quasi-symmetric stellarator repository’.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"219 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A structure-preserving particle discretisation for the Lenard–Bernstein collision operator","authors":"S. Jeyakumar, M. Kraus, M.J. Hole, D. Pfefferlé","doi":"10.1017/s0022377824000564","DOIUrl":"https://doi.org/10.1017/s0022377824000564","url":null,"abstract":"<p>Collisions are an important dissipation mechanism in plasmas. When approximating collision operators numerically, it is important to preserve their mathematical structure in order to retain the laws of thermodynamics at the discrete level. This is particularly challenging when considering particle methods. A simple but commonly used collision operator is the Lenard–Bernstein operator, or its modified energy- and momentum-conserving counterpart. In this work, we present a macro-particle discretisation of this operator that is provably energy and momentum preserving.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"22 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization","authors":"G.T. Roberg-Clark, P. Xanthopoulos, G.G. Plunk","doi":"10.1017/s0022377824000382","DOIUrl":"https://doi.org/10.1017/s0022377824000382","url":null,"abstract":"We present a stellarator configuration optimized for a large threshold (‘critical gradient’) for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"211 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature","authors":"Evan Toler, A.J. Cerfon, D. Malhotra","doi":"10.1017/s0022377824000527","DOIUrl":"https://doi.org/10.1017/s0022377824000527","url":null,"abstract":"<p>In a recent publication (Toler <span>et al.</span>, <span>J. Plasma Phys.</span>, vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"36 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kinetic stability of Chapman–Enskog plasmas","authors":"Archie F.A. Bott, S.C. Cowley, A.A. Schekochihin","doi":"10.1017/s0022377824000308","DOIUrl":"https://doi.org/10.1017/s0022377824000308","url":null,"abstract":"<p>In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span> of constituent particles is short compared with the length scale <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$L$</span></span></img></span></span> over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$lambda /L ll 1$</span></span></img></span></span>, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$beta$</span></span></img></span></span>, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (<span>viz.</span> plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline5.png\"><span data-mathj","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"28 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Progress of open systems at Budker Institute of Nuclear Physics","authors":"P.A. Bagryansky","doi":"10.1017/s0022377824000473","DOIUrl":"https://doi.org/10.1017/s0022377824000473","url":null,"abstract":"This paper is based on a report at the 2nd International Fusion Plasma Conference & 13th International Conference on Open Magnetic Systems for Plasma Confinement (iFPC & OS 2023), August 21–25, 2023, Busan, Korea and provides a brief overview of the status of work at the Budker Institute on the study of hot plasma confinement in open-type magnetic traps with a linear axisymmetric configuration. The main attention is paid to key problems: magnetohydrodynamics (MHD) stability in regimes with extremely high relative pressure, longitudinal electronic thermal conductivity, stability with respect to the development of kinetic modes and transverse transport. This paper provides an overview of the methods we are developing to address these problems, the experimental and theoretical results achieved and plans for future development. The last section of the article provides brief information about the preliminary design of the gas-dynamic multiple-mirror trap device, the development of which has been completed.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"28 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Evgeniy A. Shmigelsky, Andrej A. Lizunov, Andrey K. Meyster, Egor I. Pinzhenin, Alexander L. Solomakhin, Dmitry V. Yakovlev
{"title":"Recent results on high-β plasma confinement studies in the Gas Dynamic Trap","authors":"Evgeniy A. Shmigelsky, Andrej A. Lizunov, Andrey K. Meyster, Egor I. Pinzhenin, Alexander L. Solomakhin, Dmitry V. Yakovlev","doi":"10.1017/s0022377824000515","DOIUrl":"https://doi.org/10.1017/s0022377824000515","url":null,"abstract":"This paper is devoted to experimental studies of plasma confinement with high relative pressure (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$beta$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline2.png\"/> </jats:alternatives> </jats:inline-formula>) in the Gas Dynamic Trap (BINP, Novosibirsk). In previous high-<jats:inline-formula> <jats:alternatives> <jats:tex-math>$beta$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline3.png\"/> </jats:alternatives> </jats:inline-formula> confinement studies a maximum local <jats:inline-formula> <jats:alternatives> <jats:tex-math>$beta = 0.6$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline4.png\"/> </jats:alternatives> </jats:inline-formula> was achieved in the fast-ion turning point, contributed to by a beam-driven population of fast ions with an anisotropic distribution function. In this study the axial magnetic field profile was modified to bring the turning points closer to one another, which effectively increased the energy density of plasma and pushed the <jats:inline-formula> <jats:alternatives> <jats:tex-math>$beta$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline5.png\"/> </jats:alternatives> </jats:inline-formula> value higher. Experiments were performed for two non-standard magnetic configurations, where the axial fast-ion confinement region length was reduced by 1.5 and 2 times compared with the standard configuration. The average values of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$langle beta _{perp } rangle$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline6.png\"/> </jats:alternatives> </jats:inline-formula> over the plasma central cross-section were found to be 0.1 and 0.18, respectively, for the two configurations, with the latter value significantly exceeding the <jats:inline-formula> <jats:alternatives> <jats:tex-math>$langle beta _{perp } rangle =0.08$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000515_inline7.png\"/> </jats:alternatives> </jats:inline-formula> of the standard configuration, in which the previous record was set. Moreover, halving the fast ion confinement region almost doubled the D–D fusion proton flux from the trap centre compared with the standard configuration. The electron temperature in both new magnetic configurations was only slightly smaller than in the standard configuration. In addition, an effect of Alfvén ion–cyclotron instability (AICI) development on the pressure in the turning points is discussed. Presumably, with some decrease in mag","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"35 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hybrid electrostatic waves in linearized gravity","authors":"Chinmoy Bhattacharjee, David J. Stark","doi":"10.1017/s0022377824000539","DOIUrl":"https://doi.org/10.1017/s0022377824000539","url":null,"abstract":"<p>Linearized gravity around a rotating black hole or compact object introduces the concept of a gravitomagnetic field, which originates from the matter–current in the rotating object. Plasma in proximity to this object is subsequently subjected to motion guided by this gravitomagnetic term (where mass serves as the effective charge) in addition to the conventional magnetic field. Such an interplay of fields complicates the accessible plasma waves of the system and thus merits exploration to delineate this interplay, to identify any observable signatures of the gravitomagnetic field in weakly magnetized systems, and to motivate future numerical work in a fully relativistic setting where the effects may be stronger. In this work we analyse the dispersion of the upper and lower hybrid electrostatic waves in a plasma immersed in both magnetic and gravitomagnetic fields. In particular, we discuss the effective augmentation or cancellation of the two fields under the right conditions for the upper hybrid wave. In contrast, the lower hybrid wave experiences a frequency up-shift from the gravitomagnetic field regardless of whether it is parallel or antiparallel to the magnetic field for the studied field strengths.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"77 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140810164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}